I have $S_t = 10 + B_t$, $\beta_t = 1$, $a_t = 2B_t$, $b_t = -t - B_t^2 - 20B_t$
Then the value, $V = a_t S_t + b_t \beta_t$
Is this a self financing portfolio? Note, $B_t$ is brownian motion
I am struggling to use Ito's lemma here to show if it is.
Essentially I just need to show
$dV = (2B_t)dSt + (b_t)d\beta_t$, correct?
but how can I do this?